Jessica is 4 years older than Vanessa. Twenty years ago, Jessica was 5 times as old as Vanessa. How old is Vanessa now?
Explanation: We can use the given information to write down two equations that describe the ages of Jessica and Vanessa. Let Jessica's current age be $j$ and Vanessa's current age be $v$ The information in the first sentence can be expressed in the following equation: $j = v + 4$ Twenty years ago, Jessica was $j - 20$ years old, and Vanessa was $v - 20$ years old. The information in the second sentence can be expressed in the following equation: $j - 20 = 5(v - 20)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $v$ , it might be easiest to use our first equation for $j$ and substitute it into our second equation. Our first equation is: $j = v + 4$ . Substituting this into our second equation, we get the equation: $(v + 4)$ $-$ $20 = 5(v - 20)$ which combines the information about $v$ from both of our original equations. Simplifying both sides of this equation, we get: $v - 16 = 5 v - 100$ Solving for $v$ , we get: $4 v = 84$ $v = 21$.